Unsteady thin film flow of a fourth grade fluid over a vertical moving and oscillating belt

Purpose – The purpose of this paper is to study the thin film flow of a fourth grade fluid subject to slip conditions in order to understand its velocity profile. Design/methodology/approach – An exact expression for flow velocity is derived in terms of hyperbolic sine functions. The practical usage of the exact flow velocity is restrictive as it involves very complicated integrals. Therefore, an approximate solution is also derived using a Galerkin finite element method and numerical error analysis is performed. Findings – The behavior of fluid velocity with respect to various flow parameters is discussed. The results are not restrictive to small values of flow parameters unlike those obtained earlier using homotopy analysis method and homotopy perturbation method. Originality/value – An approximate solution based on finite element technique is derived.

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Optimal homotopy asymptotic method with application to thin film flow

Open Physics ◽

10.2478/s11534-008-0061-x ◽

2008 ◽

Vol 6 (3) ◽

Cited By ~ 78

Author(s):

Vasile Marinca ◽

Nicolae Herişanu ◽

Iacob Nemeş

Keyword(s):

Thin Film ◽

Asymptotic Method ◽

Film Flow ◽

Vertical Cylinder ◽

Thin Film Flow ◽

Analytical Technique ◽

Grade Fluid ◽

Optimal Homotopy Asymptotic Method ◽

Linear Problems ◽

Fourth Grade Fluid

AbstractA new approximate analytical technique to address for non-linear problems, namely Optimal Homotopy Asymptotic Method (OHAM) is proposed and has been applied to thin film flow of a fourth grade fluid down a vertical cylinder. This approach however, does not depend upon any small/large parameters in comparison to other perturbation method. This method provides a convenient way to control the convergence of approximation series and allows adjustment of convergence regions where necessary. The series solution has been developed and the recurrence relations are given explicitly. The results reveal that the proposed method is very accurate, effective and easy to use.

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Thin film flow of a second grade fluid in a porous medium past a stretching sheet with heat transfer

Alexandria Engineering Journal ◽

10.1016/j.aej.2017.01.036 ◽

2018 ◽

Vol 57 (2) ◽

pp. 1019-1031 ◽

Cited By ~ 45

Author(s):

Noor Saeed Khan ◽

Saeed Islam ◽

Taza Gul ◽

Ilyas Khan ◽

Waris Khan ◽

...

Keyword(s):

Thin Film ◽

Heat Transfer ◽

Porous Medium ◽

Stretching Sheet ◽

Film Flow ◽

Second Grade ◽

Thin Film Flow ◽

Second Grade Fluid ◽

Grade Fluid

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Thin Film Flow of a Third Grade Fluid with Variable Viscosity

Zeitschrift für Naturforschung A ◽

10.1515/zna-2009-9-1003 ◽

2009 ◽

Vol 64 (9-10) ◽

pp. 553-558 ◽

Cited By ~ 6

Author(s):

Sohail Nadeem

Keyword(s):

Thin Film ◽

Film Flow ◽

Variable Viscosity ◽

Nonlinear Differential Equations ◽

Third Grade ◽

Outer Side ◽

Physical Parameters ◽

Third Grade Fluid ◽

Thin Film Flow ◽

Grade Fluid

The effects of variable viscosity on the flow and heat transfer in a thin film flow for a third grade fluid has been discussed. The thin film is considered on the outer side of an infinitely long vertical cylinder. The governing nonlinear differential equations of momentum and energy are solved analytically by using homotopy analysis method. The expression for the viscous dissipation and entropy generation are also defined. The graphical results are presented for various physical parameters appearing in the problem

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